1:00, SAM-P1.1
SPECTRAL ESTIMATION UNDER NATURE MISSING DATA
J. HUNG, B. CHEN, W. HOU, L. CHEN
This paper considers the problem of estimating the autoregressive moving average (ARMA) power spectral density when measurements are corrupted by noises and with missing data. The missing data model is based on a probabilistic structure with unknown. In this situation, the spectral estimation becomes a highly nonlinear optimization problem with many local minima. In this paper, we use the global search method of genetic algorithm (GA) to achieve a global optimal solution of this spectral estimation problem. From the simulation results, we have found that the performance is improved significantly if the probability of data missing is considered in the spectral estimation problem.

1:00, SAM-P1.2
JOINT DETECTION AND HIGH RESOLUTION ML ESTIMATION OF MULTIPLE SINUSOIDS IN NOISE
M. MACLEOD
Harmonic analysis, the analysis of signals which consist of a sum of sinusoids (or complex sinusoids) with additive white or colored noise, is a much studied problem, with many important applications. Nevertheless, existing approaches have significant limitations. In many, the model order (number of sinusoids) is assumed known, and in most cases Additive White Gaussian Noise (AWGN) is assumed. We present a method for jointly determining the model order and estimating the sinusoid parameters in white or colored noise. It uses the notch periodogram in an iterative detection and estimation algorithm. It uses an explicit detection test based on an estimate of the noise PDS, which is obtained by smoothing the logarithm of the notch periodogram.

1:00, SAM-P1.3
FAST IMPLEMENTATION OF TWO-DIMENSIONAL APES AND CAPON SPECTRAL ESTIMATORS
E. LARSSON, P. STOICA
The matched-filterbank spectral estimators APES and CAPON have recently received considerable attention in a number of applications. Unfortunately, their computational complexity tends to limit their usage in several cases -- a problem that has previously been addressed by different authors. In this paper, we introduce a novel method to the computation of the 1D and 2D APES and CAPON spectra, which is considerably faster than all existing techniques. Numerical examples are provided to demonstrate the application of APES to synthetic aperture radar (SAR) imaging, and to illustrate the reduction in computational complexity provided by our implementation.

1:00, SAM-P1.4
DECIMATION AND SVD TO ESTIMATE EXPONENTIALLY DAMPED SINUSOIDS IN THE PRESENCE OF NOISE
S. FOTINEA, I. DOLOGLOU, G. CARAYANNIS
A new state-space method for spectral estimation that performs decimation by factor two while it makes use of the full set of data available is presented in this paper. The proposed method, called DESE2, is based on Singular Value Decomposition in order to estimate frequency, damping factor, amplitude and phase of exponentially damped sinusoids in the presence of noise. The DESE2 method is compared against some previously proposed methods for spectral estimation that lie among the most promising methods in the field of spectroscopy, where accuracy of parameter estimation is of utmost importance. Experiments performed on a typical simulated NMR signal prove the new method to be more robust, especially for low signal to noise ratio. The new method outperforms the other two not only by presenting lower failure rates but also by incorporating enhanced discriminative analysis while at the same time it benefits from the use of the full data set.

1:00, SAM-P1.5
A FAMILY OF COSINE-SUM WINDOWS FOR HIGH-RESOLUTION MEASUREMENTS
H. ALBRECHT
Special windows are used in spectral analysis to reduce the effect of spectral leakage. Windows with low sidelobe amplitude are necessary for the detection of small signals when highly dynamic spectra are concerned. The design of a family of cosine-sum windows with minimum sidelobes is described. The coefficients and selected parameters for windows with a peak sidelobe level between -43 dB and -289 dB are stated.

1:00, SAM-P1.6
MULTITAPER ESTIMATION OF BICOHERENCE
Y. BIRKELUND, A. HANSSEN, E. POWERS
The statistical properties for bicoherence estimation are shown to be strongly connected to the properties of the power- and bispectral estimator used. Data tapering will reduce spectral leakage and frequency smoothing will reduce the variance. It is shown that correct normalization is essential to ensure unbiased results. The multitaper approach is shown to be superior to other non-parametric estimators for bicoherence estimation.

1:00, SAM-P1.7
SINUSOIDAL FREQUENCY ESTIMATION USING FILTER BANKS
A. TKACENKO, P. VAIDYANATHAN
One problem of great interest to the signal processing community is that of estimating the frequencies of sinusoids buried in noise. Traditional methods applied to a fullband signal fail to estimate accurately when the signal-to-noise ratio (SNR) or spacing between frequencies is small. They also fail when the noise is not white and its statistics are unknown. In this paper, we consider these methods when applied to the subbands of a filter bank and show that, through proper choice of analysis filters, the local SNR and frequency spacing increase by the decimation ratio. We also show that the subband noise processes will be, on average, more ``white'' than the fullband one in terms of the spectral flatness measure. This suggests that if the noise statistics are unknown, there will be less error by estimating in the subbands as opposed to the fullband. Experimental results support this theory, as we shall show.

1:00, SAM-P1.8
ALMOST SURE IDENTIFIABILITY OF MULTIDIMENSIONAL HARMONIC RETRIEVAL
N. SIDIROPOULOS, T. JIANG, J. TEN BERGE
Two-dimensional (2-D) and more generally multi-dimensional harmonic retrieval is of interest in a variety of applications. The associated identifiability problem is key in understanding the fundamental limitations of parametric high-resolution methods. In the 2-D case, existing identifiability results indicate that, assuming sampling at Nyquist or above, the number of resolvable exponentials is proportional to $I+J$, where $I$ is the number of (equispaced) samples along one dimension, and $J$ likewise for the other dimension. We prove in this paper that the number of resolvable exponentials is roughly $IJ/4$, almost surely. This is not far from the equations-versus-unknowns bound of $IJ/3$. We then generalize the result to the $N$-D case for any $N > 2$, showing that, under quite general conditions, the number of resolvable exponentials is proportional to total sample size, hence grows exponentially with the number of dimensions.

1:00, SAM-P1.9
RECURSIVE SINGLE FREQUENCY ESTIMATION
J. KLEIN
A new divide-and-conquer method for estimating the frequency of a single complex sinusoid in additive uncorrelated noise is proposed. Its computational complexity is comparable to previous fast methods (roughly 2N complex multiplies and log2(N) arctangents for N a power of 2). However, it nearly achieves the Cramer-Rao bound for a wider range of input frequency and signal-to-noise-ratio (SNR) values. Simulations are presented to demonstrate its performance.